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By Frances Jane Cromwell, D. J. McAdam, G. W. Geil

In a series of papers, the authors and their associates have shown that the technical cohesion limit is affected by the same four factors that affect the flow stress, namely, the stress system, plastic deformation, temperature, and the strain rate.16-28 Moreover, each of these factors affects the technical cohesion limit in the same way that it affects the flow stress,t The influence of any one of these factors may be represented by a curve of cohesion limits, although only one point on the curve may represent actual fracture. As the term ilfracture stress' has come into use with the same significance as 'ctechnical cohesion limit," the authors are here using the shorter term with the understanding that it does not always refer to actual fracture. This paper presents the results of an investigation of the flow of notched and unnotched specimens betqrcen yield and fracture, A study has thus been made of the flow and fracture of metals as affected by the stress system, and of the ductility of metals as affected by the stress system throughout plastic deformation. Since two of the principal stresses were equal (S2 = S3), the stress systems can be represented in terms of the radial stress ratio, the ratio of the transverse radial stress s3 to the longitudinal stress S1.* The results of the experiments are represented by a series of their flow-stress curves for each Of the metals investigated, and these diagrams have been used for the development Of Other diagrams Of various types. Ludwik was the first to suggest that fracture occurs when the flow stress becomes equal to a technical cohesion limit. Although Ludwik was incorrect in his view that the technical cohesion limit depends only on the amount of plastic deformation and not On the stress system, he was 'Orrect in his view that the flow-stress curve for any stress system terminates at a point representing a technical cohesion limit. The authors have seen some recent references to assertions by other investigators that a point representing the fracture stress need not be on the flow-stress curve. The Ludwik principle, however, "auld Seem to be axiomatic, provided that the flow Stress and fracture stress are properly defined and that the fracture stress is properly determined. Disregard Of this principle has led to some untenable theories Of criteria for fracture. When a metal is very ductile, the conventional method of determining the ductility and fracture stress by dividing the breaking load by the sectional area after fracture, generally gives values that are much too high. With some metals and in some conditions, the fracture stress thus determined may be two or more times the

Jan 1, 1949

By Franklin H. Allison

The influence of cobalt and nickel on the properties of steel might be readily expected to be very similar. The two elements occupy close and somewhat unusual positions in the periodic table, their chemical behavior and compounds are so completely analogous and their various physical properties, including the ferro-magnetic characteristic, show such 3 remarkable correspondence, that there is no doubt of a strong resemblance existing between these two metals. However, the variety of properties that are obtained from steel is due largely to the fact that the element iron possesses allotropic forms. Alloying elements that affect these allot ropic forms, or alter the nature of the allotropic changes, exert a profound influence on the resulting steel. In the case of nickel and cobalt, although these elements are very similar chemically and physically, it is found that they differ distinctly in their individual effects on the critical points of iron. Both nickel and cobalt form a series of homogeneous solid solutions with iron at temperatures above 1500" F. The difference in their behavior does not occur until changes begin to take place in the solid state below this temperature. An inspection of the respective thermal equilibrium diagrams at the lower temperatures makes the opposite effects of nickel and cobalt clearly evident. Effect of Nickel and Cobalt in Binary Alloys with Iron The binary diagram of iron-nickel has been investigated by a number of workers. The lower temperature portion in Fig. 1 is reconstructed from the data of D. and H, Hanson.1 The diagram of iron-cobalt, shown in Fig. 2, is taken from the work of Ruer and Kaneko.2 Masumoto3 has recently discovered a lower critical point in cobalt and this has been added to the diagram. In both diagrams the space lattice structures as determined by Andrews4 have been included. It is interesting to note

Jan 1, 1927

John M. Cairns, in an interesting letter dated June. 19, 1918, tells us of his experiences in Italy. He says, "It may interest you to know I came out to Italy after being on the Afghan frontier of Indian Baluchistan, in August last year, and for some time was posted at Turin as Railway Transport officer. At that time Turin was in the toils of the riots which were the forerunners and preliminaries which led up to the great Italian retreat (Capretto). Since then I have been all over Italy from (deleted by the censor) in Transportation intelligence, and now have just been transferred to the Directorate of Requisitions and Hirings, which now permits great opportunities of going nearly all over Italy (deleted by the censor). My address is L. of C. Branch, D. R. & H., A. P. 0. L/1, I. E. F.

Jan 9, 1918

By J. M. Dumore

If in a vertical, downward miscible displacement, the transition zone between the displacing and displaced fluids is neglected, a criterion for stable displacement can be obtained by considering a small hypothetical protrusion of one of the fluids into the other. This criterion leads to the definition of the well-known critical rate, uc = kg p/p. The consideration is further extended by taking into account the transition zone that develops as a result of diffusion and mixing. A generalization of the previous criterion leads to the definition of another characteristic rate, the stable rate, which in actual miscible drives will be less than the critical rate. In such drives, the entire transition zone is stable at rates less than the stable rate. At rates between the stable and critical rates, the displacement is only partly stable, i.e. part of the transition zone adjacent to the displaced fluid is in an unstable position. From that part of the transition zone viscous lingers will develop. At rates greater than the critical rate the entire displacement is unstable and viscous lingers will develop more strongly. Results of laboratory experiments are in agreement with the expected behavior based on the theoretically deduced stability of the displacement. INTRODUCTION The simplest form of miscible drive in an oil-bearing formation is the injection of a fluid that is completely miscible* with the oil under reservoir conditions. In general, such a fluid, a solvent for example, is less dense and less viscous than the oil present in the formation. If it is injected into a horizontal homogeneous layer, gravitational forces will lead to the formation of a gravity tongue of solvent in the upper part of the layer and the adverse solvent-oil viscosity ratio will cause viscous fingers to develop. If, however, the solvent is injected up-structure into ,a dipping layer, gravity has a favorable effect, because it tends to keep the less dense solvent up-structure. Tongue formation and viscous fingering are consequently reduced and it is even possible that they will be suppressed completely. Viscous fingering and gravity tonguing are the consequences of the instability of the displacement. A stable displacement cannot result in growing viscous fingers and/or growing gravity tongues. Since large amounts of oil can be bypassed if there is viscous fingering and/or gravity tonguing, the stability of a miscible drive is very important with respect to the recovery efficiency of the drive. The stability is of particular importance in miscible-slug drives, as it determines how quickly the miscible slug between the displaced and displacing fluids will be distorted and broken up, after which the drive is no longer completely miscible. Stability is thus a most important factor in determining the success of a miscible drive, and it is considered that the aspects of stability considered in this paper will make a useful contribution to existing theories. Consideration is given only to vertical downward displacements, in which no gravity tongues can develop and which are therefore simpler than downward displacements in sloping layers. THEORY CRITERION FOR STABLE DISPLACEMENT Let us consider a vertical column of a homogeneous permeable medium saturated with oil. A solvent less dense and less viscous than the oil is injected at the top of the column at a constant rate; in the column the velocities of oil and solvent are assumed to be uniform. Diffusion and mixing of oil and solvent will at first be neglected, i.e. we assume that solvent and oil are divided by a sharp interface. An additional assumption is that the interface is horizontal. Continuity of pressures exists at the interface, because no capillary forces are present between the two miscible fluids. Consequently, at the interface (Z = I)):** Ps = Po - P-where Ps is the pressure at the solvent side and

Jan 1, 1965

(The following list contains the names of those members of the Institute of whose connection with military service we have only recently become acquainted; it also includes the names of a few who have recently been promoted or transferred, indicated by a *. A complete list was published in the Year Book, issued as a supplement of the Bulletin for March, 1915.) ADAMS, ARTHUR K., Lieut., Co. 2, E. 0. T. S., Camp Humphreys, Va. AMIDON, CLAUDE E., 11th Training Co., Casual Camp, Camp Cody, N. M *BARBOUR, P. E., Capt., Engineer Corps, U. S. A. *BENHAM, W. M., Master Engr., Headquarters Dept., 115th Engrs. A. E. F., Care Postmaster, N. Y. BICKNELL, H. L., Pvt., Co. D, 27th Engrs., Camp Leach, D. C. *BLANDY, S. H. B., Lieut., Royal Horse Artillery, B. E. F.

Jan 10, 1918

By William R. Webster

At the Richmond mecting in February, 1901, I presented for discussion the proposed rail-specifications of Committee No. 1 of the American Section of the International Association for Testing Materials, with a review of their work, and other matters relating to the heat-treatment and chemical composition of steel (Trans., xxxi., 455). In order to bring out the views of our members on the important points referred to, I offered for discussion the following questions and comments (trans., xxxi., 972): " 1. The advantages to be gained by using more metal in the flanges and web of the heavier sections of rails.

Jan 1, 1903

By Edward B. Durham

At the Richmond mecting in February, 1901, I presented for discussion the proposed rail-specifications of Committee No. 1 of the American Section of the International Association for Testing Materials, with a review of their work, and other matters relating to the heat-treatment and chemical composition of steel (Trans., xxxi., 455). In order to bring out the views of our members on the important points referred to, I offered for discussion the following questions and comments (trans., xxxi., 972): " 1. The advantages to be gained by using more metal in the flanges and web of the heavier sections of rails.

Jan 1, 1903

By T. J. Koppenaal, M. E. Fine

The critical resolved shear stress of aCu-A1 single crystals has been investigated as a function of composition, testing temperature, and strain rate. The strength, and its temperature and strain rate dependency increase markedly with aluminum content. The solid solution strengthening at 4.2°K is much larger than at room temperature. The activation energy for the low temperature dislocation cutting process increases from about 0.17 ev for a 0.5 at. pct A1 alloy to about 0.50 ev for a 14 at. pct A1 alloy. This result is attributed to an increase in the width of extended dislocations due to the known decrease in the stacking fault energy. In addition, the activation volumes at 4.2 and 77°K decrease with aluminum additions. Concerning the solid solution strengthening in the 296° to 373°K range, no definite conclusions are reached, but it is suggested that subgrains and cutting of subgrains are important. In a previous paper,' the authors reported that adding aluminum to copper produces two types of strengthening: a yield point effect and an increase in the lower yield stress. This behavior is illustrated in Fig. 1 by shear stress-shear strain curves of furnace-cooled single crystals of pure copper and Cu-14 at. pct A1. The yield point effect, At, was thoroughly studied previously1 and shown to be associated with short-range order. The present paper reports an investigation of the lower-yield stress in aCu-A1 single crystals as a function of composition, testing temperature, and strain rate. EXPERIMENTAL PROCEDURE Single cryski1 tensile specimens were prepared in the same manner as previously described.l Briefly,

Jan 1, 1962

By M. F. Fogler

An attempt to duplicate Rawdon and Mutchler's experiments showing a reversal of hardness with continued rolling gave negative results, indicating that the phenomenon is not general but depends, probably, on local conditions of rolling. IN A recent paper, Rawdon and Mutchler1 gave some exceptionally interesting results on the Brinell and scratch hardness of severely cold-worked metals. In their work, they found that, on continued cold rolling, the metal hardened up to a particular point and then reversed and became softer; this was true for both Brinell and scratch hardness values. The generally reported behavior2 of metals, with respect to Brinell tests on cold-worked material, is that the metals harden up to a certain point and then, on further cold rolling, no change in Brinell hardness occurs. Jeffries and Archer3 state that there is little difference between the scratch hardness of annealed and cold-worked metals; the work of Faust and Tammann4 also indicated no difference between-the hardness of annealed and cold-worked copper. Rawdon and Mutchler found, when they plotted the reduction ratio (initial thickness divided by thickness after rolling) against the hardness value for the cold-rolled material, that the hardness number increased up to a reduction ratio of about 3 and then decreased and became even smaller than that for the annealed metal. This behavior was reported for both scratch and Brinell hardness; Figs. 1 and 2 show their results for Brinell hardness on the metals for which they published data. This is an exceptionally interesting phenomenon, if it occurs under all conditions of rolling, and would have an important bearing on the practice of cold

Jan 1, 1925

E. DEGOLYER,-New York, N. Y. (written discussion*).-Since the eastern part of the Gulf Coastal Plain is receiving considerable attention from various operators at the present time, it occurs to me that it brief review of most recent operations may be of interest in this connection, as well as a discussion of some of the points suggested by Mr. Hager. During the latter part of January, 1918, the Alahoma Oil Co. completed and abandoned a 3400-ft. (1036-m.) dry hole in Section 25, Township-8 North, Range 1 West. This well was drilled near the axis of the

Jan 4, 1918

By F. Weinberg

INTEREST is currently being directed toward grain boundary morphologies in zinc in terms of grain boundary facetingl and grain boundary energies.' Some years ago the present author attempted to measure grain boundary energies in 99.999 pct purity Zn as a function of boundary angle, using the standard procedure of measuring equilibrium angles of the boundary traces at triple points. This followed an investigation he carried out on preferential melting of |H (112) Fig. 1—Electron transmission micrograph of a stacking fault, grain boundary intersection in copper. GRAIN BOUNDARY STACKING FAULT Fig. 2—Schematic representation of the intersection of Fig. 1, indicating inclination angles 0 and trace angles $. specimens were prepared by the Bollman technique in an electrolyte of 70 pct methanol, 30 pct HNO3 main-tained at -30°C. The interfacial free energy of the high angle grain boundary and of the stacking fault is assumed to be thermodynamically equivalent to the corresponding in-terfacial tensions. In terms of the true dihedral angles & between the intersecting interfaces, the equilibrium of interfacial tensions in the direction parallel to the stacking fault yields: ysF = -ygb(cos F1+ cos ±cosF2) Here, ysF is the stacking fault free energy and ygb is the grain boundary free energy, assumed equal on both sides of the intersection. Forces acting normal to the grain boundary, of the form ??gb/?F,l are assumed negligible as the grain boundary remains straight for a considerable distance on either side of the intersection. The micrograph of Fig. 1 may actually consist of several closely spaced stacking faults on the same slip plane. The actual point of intersection between the grain boundary and the first stacking fault, and the equilibrium configuration of the intersection, should not be affected by the presence of the other faults, as

Jan 1, 1970

By John J. Stokes

Literature on the electrolysis of aluminum from cryolite melts and on the structure of these melts is surveyed critically. Data on density, freezing point, and other properties are reviewed. Theories of the electrolysis are examined in the light of these data. Two theories are presented which account equally well for the observations. * * * * In the early days, the process was thought of as a simple one. The actual mechanisms must be tremendously more complex. This paper is devoted to a rather narrow part of the whole subject, namely, what ions are present in the bath, and by what mechanism the current is carried.

Jan 4, 1958

By J. W. Pamplin

SOME 40 miles east of Tampa is the center of the Florida pebble phosphate deposits. These are of Pliocene age and consist of several members of the Bone Valley formation.' Physically the phosphate-bearing formation, locally called the “matrix," varies in thickness from nothing to about 25 ft., usually averages 10 ft., and consists mainly of clay, quartz and phosphate pebble, the latter particles varying in size from colloidal to one inch diameter. The pebbles range in color from dark gray, through white, to cream, and in hardness from that which must be broken with a hammer to that which can be scratched with the fingernail. They assay from 66 to 80 per cent bone phosphate of lime (called "B.P.L." in the trade) or tricalcium phosphate (Ca3P2O8) and are secondary apatites. They form from 15 to 50 per cent by weight of the matrix. Over the matrix lies a varying thickness (5 to 40 ft.) of overburden composed of quartz and clay. Briefly, mining consists of two operations2 in open pits about 200 ft. wide by ½ mile or more in length. In the first step overburden is removed by large electric draglines at the rate of about 700 cu. yd. per hour. This is followed closely by hydraulic mining of the matrix at the rate of about 300 cu. yd. per hour. This matrix yardage is moved from an improvised sump in the floor of the pit to an ore-dressing plant, some- times a mile distant, by one, two or three "pit-cars" (pumping units) working on a 12-in. pipe line called the "rock line" to distinguish it from the high-pressure water line feeding the hydraulic giants, which is known as the “hydraulic line." This 700 yd. of overburden and 300 yd. of matrix-1000 yd. in all- amounts to about 1500 tons of material moved each hour. The over- burden is dumped into the mined-out pit alongside the pit being mined. The matrix moves to the ore-dressing plant at the rate of about 7 ½ long tons in 4000 gal. of water per minute-a ratio of approximately one to two by weight, or one to six by volume. This constitutes the "mill heads," but in the pebble district it is called the "matrix."

Jan 1, 1938

By L. C. Brown, A. J. Stewart

Phase transformations have been studied in Ag-Zn alloys quenched from the high-temperature bcc 0 phase and lying in the composition range 37.4 to 50.0 at. pct Zn. On quenching, the alloy with the lowest zinc content transformed to massive a (fcc); all other alloys formed the ordered (3' phase. On deformation, a martensitic reaction took place forming a close-packed structure. At Lou' zinc contents transformation to this structure was complete. However, above 43 at. pct Zn a p.rogressively increasing amount of ß' was retained following deformation. The close-packed structure was fcc at lower zinc contents (under 47 at. pct Zn) and either hcp or a mixture of fcc and hcp at high zinc concentrations. The structures produced by cold working were unstable and on aging transformed to the ß' phase or the complex hexagonal to phase. For low zinc contents (under 43 at. pct) the fcc st-ructure transformed directly to the equilibrium To phase. With higher zinc contents, some 13' was retained following defownation, and on aging the amount of this phase relative to the close-packed structure increased. On further aging both structures transformed cornpletely to PO. Metallographic examination indicated that the nature of the deformation product depended very markedly on the mode of deformation. Tensile deformation gave a microstructure characteristic of thermal martensite. KING and Massalski1 have shown that an alloy of Ag-50 at. pct Zn quenched from the high-temperature bcc ß phase undergoes a low-temperature ordering reaction forming ß' which can be retained to room temperature. On deformation an hcp phase is produced, although this is unstable and the structure reverts completely to ß' on aging. In the present paper, the work of King and Massalski is extended to cover a wide composition range in the p phase, observations being made of the structure of the quenched 13 and of the effects of deformation and aging. The relevant portion of the Ag-Zn phase diagram is shown in Fig. 1. King and Massalski have shown that close to stoichiometry the ß' phase is the equilibrium structure at low temperatures. The approximate composition range of this phase, taken from a recent paper by Pops and Massalski,3 is shown on the phase diagram. The locations of atom sites are very similar in the ß' and to structures, and the 4, structure can be derived from the 0' structure by a small movement of atoms mainly in the direction of the cube diagonal.4'5 However, the probability of filling any particular atom site by a silver or a zinc atom is markedly different in the two structures. The structure can be considered partly ordered but the arrangement of the ordered atoms is completely different from that in the p' structure and transformation from ß' to requires a large fraction of the atoms to change position. It has been shown that the ß' transformation is thermally activated involving normal nucleation and growth processes.5,8 Massalski and Barrett7 have shown that in the Cu-Zn binary the (3 phase can be retained in the ordered state to room temperature over a wide composition range. On deformation a new close-packed phase is produced, the structure varying from fcc to a mixture of fcc + hcp to hcp alone with increasing zinc concentration. It appears that an ordering reaction is necessary to retain the bcc phase to room temperature. In CU-Ga,8 the bcc phase cannot be retained to low temperatures as it transforms by a massive reaction above the ordering temperature of the ß phase. The structure of the massive phase is very similar to that in Cu-Zn, varying from fcc to fcc + hcp to hcp with increasing zinc concentration. Similar structures have also been observed in CU-A1,9 Ag-Cd,10,11 and Ag-Al.12 EXPERIMENTAL The alloys were prepared by melting fine silver (99.99 pct purity) and electrolytic zinc (99.999 pct

Jan 1, 1969

By W. B. Triplett, H. I. Aaronson, G. M. Andes

A detailed morphological study has been made of the pro-eutectoid TiCr, and the eutectoid reactions in a Ti-17.42 pct Cr alloy isothermally transformed at temperatures from 775° through 5561°C. The morphologies of proeute,ctoid TiCr2 were found to be subject to description by the Dube morphological classification system. Grain boundary allotriomo.lphs are the dominant plpoeutectoid morphology throughout the temperature range investigated. lntragranular plates, and especially Widmanstatten sideplates, form only in small numbers. This morphological pattern differs markedly from that of the proeutectoid a reaction in hypoeutectoid Ti-Cr alloys (AIME Trans., 1957, vol. 209, p. 1227; 1958, vol. 212, p. 624), in which plates form prolifically throughout wide ranges of temperature. The eutectoid reaction is nonlamellar in character at 675°C. An increasingly prominent lamellar component develops at lower temperatures. The proeutectoid TiCr 2 and the eutectoid transformations have been studied metallographically in a hypereutectoid titanium-chromium alloy. This investigation was undertaken with the immediate objective of comparing these transformations with their counterparts in hypoeutectoid titanium-chromium alloys, studies of which have been recently completed.1,2 It was also intended, however, to contribute to the general literature on transformations of these types. Especially in the proeutectoid case, this literature is still sufficiently sparse to make difficult the testing of generalizations on the mechanisms of these transformations. TiCr, is the only intermetallic compound in the titanium-chromium system.3-5 The TiCr2 phase field extends to a maximum temperature of 1350°C) and encompasses the approximate composition range of 62 to 68 pct Cr at lower temperatures.3'4 At temperatures below 1000°C, TiCr2 has a MgCu,-type fcc structure, with 24 atoms comprising a unit cell.6,7 Only fragmentary observations on the morphology of proeutectoid TiCr2 have been previously reported. An observation which is of considerable importance with respect to the results obtained during the present investigation was made, however, on anisother-mally transformed alloys with high chromium (48 to 70 pct Cr) contents.3"8 Despite the occurrence of extensive impingement, it is apparent that a substantial proportion of the proeutectoid TiCr, which precipitated in these alloys grew in the form of Widmanstatten plates. Several observations have been made on the eutectoid reaction in hypereutectoid alloys during investigations of the titanium-chromium phase di-

Jan 1, 1961

By H. N. Wolcott

Among the many cases of replacement of one mineral by another, that of quartz or silicates by pyrite, or even other sulphides, is not uncommon, but the reverse of this process does not appear to have been recorded, even if it has been observed. It seemed to the writer, therefore, that the case described below was worthy of record. Fig.1. GROUndALass of chalcopyrite (C) containing Rounded GRAINs of TYRITE (P) SHOWING DEFFERENT DEGREES OF REPLACEMENT BY QUARTZ (($), AND ALSO QUARTZ VEINLETS CUTTING THROUGH THE PYRITE. (PHOTOGRAPHED BY REFLECTED LIGHT.) The specimens described in this paper were obtained by R. B. Morton of Idaho Springs, Colo., from the Old Town mine, in Russell, Gulch, and ;re in the collection of Cornell University, where the writer studied them. In the rough, the specimens appeared to consist largely of chalcopy-rite. with some grains of tetrahediite. The polished surface of some of

Jan 1, 1918

Fred D. DeVaney (Magnetic Roasting of Iron Ores, P. 1219) has presented several other AIME papers, all of them concerned with grinding and concentrating problems. He is chief metallurgist, Pickands Mather & Co., at Hibbing Minn., after working for the U. S. Bureau of Mines at Tuscaloosa, Ala., and Rolla, Mo., as a junior metallurgist and a metallurgist. DeVaney started as a research metallurgist with Pickands Mather in 1942. He set up the first laboratory in the Lake Superior district devoted to taconite concentra¬ [ ] tion, his major interest. He has been an AIME member since 1923, holding various offices, including the first presidency of the Minnesota Section. DeVaney has a Bachelor's in Mining, and Master of Science earned at the University of Alabama in 1924. He is a member of the Engineers Club of Northern Minnesota and plays golf for relaxation and enjoyment.

Jan 1, 1952

By Neil H. Cole

Cost and price inflation and financial gearing through loans are characteristic of modern resources projects. Conventional discounted cash flow and 1P.R analyses, in real terms, and without financing, have inadequacies which can yield misleading results. The degree of improvement in value for project equity owners is limited to the value of the additional tax benefit accorded through the financing instrument used. Debt financing may be low in price and value, but its priority means that the equity owners assume a higher risk, thereby increasing the cost, or price, of their capital. The cost of equity capital, or investment hurdle rate, is related to the Capital Asset Pricing Model. Distortions do occur, with inflation, due to depreciation effects, which can cause the adoption of misleading project rate of return or hurdle rate criteria. For investment decisions, the greatest accuracy possible in forecasting is essential, especially for inflation rates,

Jan 1, 1985

By Irwin Roman

Numerous results and formulas have been published for analyzing seismic records, but most of them apply only to large-scale phenomena such as are encountered in studying earthquakes. In a few cases,' formulas have been published for some of the simpler structures. In the present paper, an attempt will be made to analyze several types of structures without using methods more advanced than those of a first course in calculus. In tracing a disturbance through a medium, it is almost always possible to base the analysis on Fermat's Principle of Extreme Time, which states that waves of displacement travel between points in such a manner as to make the time of travel an extremum with respect to all neighboring paths. In the simpler cases, comprising most of those used in optics or geophysical prospecting, this time is a minimum and the principle is often referred to as the Principle of Least Time. Within a homogeneous medium, having a uniform speed of transmission of the disturbance in all directions and throughout the medium, the paths are straight and are refracted at the interfaces in accordance with the Snell law of refraction, which states that the ratio of the sine of the angle, made by the ray with the normal to the interface, to the speed of transmission is the same on both sides of the interface. Thus, in any medium composed of homogeneous sections, this same ratio has a constant value at all points. In particular, if all interfaces are horizontal, it is apparent that the angles of incidence are the angles made by the ray with the vertical direction. Furthermore, the incident ray, the refracted ray and the normal to the interface are all in the same plane at each refraction,

Jan 1, 1934

By G. Ferrara

The reserves of lead and zinc ores in the metalliferous district of Iglesias in south-western Sardinia are today estimated at about 30 million tons, grading from 4 to 10% Pb + Zn. Of these reserves, about 40% are in the mines owned by AMMI Sarda S.p.A. The working of these resources goes back to ancient times. Not infrequently, traces of old Roman workings and remains of ancient implements are come upon in the higher parts of some of the ore bodies. Exploitation of these mines on larger scale, however, dates from the middle of the 18th century. Initially, the more accessible zones of the ore bodies and the richer ores were worked - the galena and the rich oxidized ores (calamine* with 25-35% Zn), which were often found in large masses, the enormous empty cavities of which still remain. The poorer grade deposits have been gradually rendered workable by the development of technology - the perfecting of the

Jan 1, 1970